Question

A statistics practitioner took a random sample of 57 observations from a population whose standard deviation is 27 and computed the sample mean to be 97.

Note: For each confidence interval, enter your answer in the form (LCL, UCL). You must include the parentheses and the comma between the confidence limits.

A. Estimate the population mean with 95% confidence.

Confidence Interval =

B. Estimate the population mean with 95% confidence, changing the population standard deviation to 51;

Confidence Interval =

C. Estimate the population mean with 95% confidence, changing the population standard deviation to 8;

Confidence Interval =

Answer 1

Answer:

a)

Xbar = 97

n = 57

standard deviation = 27

For 95% confidence interval Z = 1.96

95% confidence interval for is - Z * / sqrt(n) < < + Z * / sqrt(n)

now substitute values

97 - 1.96 * 27 / sqrt(57) < < 97 + 1.96 * 27 / sqrt(57)

89.9906 < < 104.0094

Confidence interval : ( 89.9906 , 104.0094)

b)

standard deviation = 51

Now for 95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

97 - 1.96* 51 / sqrt(57) < < 97 + 1.96 * 51 / sqrt(57)

83.7600 < < 110.2400

Confidence interval : (83.7600 ,110.2400)

c)

Now standard deviation = 8

95% confidence interval for is

- Z * / sqrt(n) < < + Z * / sqrt(n)

substitute values

97 - 1.96* 8 / sqrt(57) < < 97 + 1.96 * 8 / sqrt(57)

94.9231 < < 99.0769

Confidence interval : (94.9231 , 99.0769)